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dc.contributor.authorYust, Jasonen_US
dc.date2018-05-23
dc.date.accessioned2020-05-01T20:19:25Z
dc.date.available2020-05-01T20:19:25Z
dc.date.issued2020-07-01
dc.identifier.citationJason Yust. 2020. "Generalized Tonnetze and Zeitnetze, and the Topology of Music Concepts." Journal of Mathematics and Music, https://doi.org/10.1080/17459737.2020.1725667
dc.identifier.issn1745-9737
dc.identifier.urihttps://hdl.handle.net/2144/40514
dc.description.abstractThe music-theoretic idea of a Tonnetz can be generalized at different levels: as a network of chords relating by maximal intersection, a simplicial complex in which vertices represent notes and simplices represent chords, and as a triangulation of a manifold or other geometrical space. The geometrical construct is of particular interest, in that allows us to represent inherently topological aspects to important musical concepts. Two kinds of music-theoretical geometry have been proposed that can house Tonnetze: geometrical duals of voice-leading spaces and Fourier phase spaces. Fourier phase spaces are particularly appropriate for Tonnetze in that their objects are pitch-class distributions (real-valued weightings of the 12 pitch classes) and proximity in these space relates to shared pitch-class content. They admit of a particularly general method of constructing a geometrical Tonnetz that allows for interval and chord duplications in a toroidal geometry. This article examines how these duplications can relate to important musical concepts such as key or pitch height, and details a method of removing such redundancies and the resulting changes to the homology of the space. The method also transfers to the rhythmic domain, defining Zeitnetze for cyclic rhythms. A number of possible Tonnetze are illustrated: on triads, seventh chords, ninth chords, scalar tetrachords, scales, etc., as well as Zeitnetze on common cyclic rhythms or timelines. Their different topologies – whether orientable, bounded, manifold, etc. – reveal some of the topological character of musical concepts.en_US
dc.language.isoen_US
dc.publisherTaylor & Francisen_US
dc.relation.ispartofJournal of Mathematics and Music
dc.subjectApplied mathematicsen_US
dc.subjectPerforming arts and creative writingen_US
dc.subjectTonnetzen_US
dc.subjectTopologyen_US
dc.subjectGeometryen_US
dc.subjectFourier transformen_US
dc.subjectVoice leadingen_US
dc.titleGeneralized Tonnetze and Zeitnetze, and the topology of music conceptsen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1080/17459737.2020.1725667
pubs.elements-sourcemanual-entryen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Fine Artsen_US
pubs.organisational-groupBoston University, College of Fine Arts, School of Musicen_US
pubs.publication-statusPublisheden_US
dc.identifier.mycv528550


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